Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

A Compact Defected Ground Microstrip Device with Photonic Bandgap Effects

Filters and other devices using photonic bandgap (PBG) theory are typically implemented in microstrip lines by etching periodic holes on the ground plane of the microstrip. The period of such several holes corresponds to nearly half the guided wavelength of the transmission line. In this paper we study the effects of miniaturization of the PBG device by meandering the microstrip line about one single hole in the ground plane. A comparison of the S-parameters and dispersion behavior of the modified geometry and a conventional PBG device with a straight microstrip line shows that these devices have similar behaviors.

Crystallite size effects in stacking faulted nickel hydroxide and its electrochemical behaviour

P-Nickel hydroxide comprises a long range periodic arrangement of atoms with a stacking sequence of AC AC AC-having an ideal composition Ni(OH)(2). Variation in the preparative conditions can lead to the changes in the stacking sequence (AC AC BA CB AC AC or AC AC AB AC AC) This type of variation in stacking sequence can result in the formation of stacking fault in nickel hydroxide. The stability of the stacking fault depends on the free energy content of the sample. Stacking faults in nickel hydroxide is essential for better electrochemical activity. Also there are reports correlating particle size to the better electrochemical activity. Here we present the effect of crystallite size on the stacking faulted nickel hydroxide samples. The electrochemical performance of stacking faulted nickel hydroxide with small crystallite size exchanges 0.8e/Ni, while the samples with larger crystallite size exchange 0.4e/Ni. Hence a right combination of crystallite size and stacking fault content has to be controlled for good electrochemical activity of nickel hydroxide. (C) 2008 Elsevier B.V. All rights reserved.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of the AlgerBrush II rotating burr as a tool for inducing ocular surface failure in the New Zealand White rabbit

The New Zealand White rabbit has been widely used as a model of limbal stem cell deficiency (LSCD). Current techniques for experimental induction of LSCD utilize caustic chemicals, or organic solvents applied in conjunction with a surgical limbectomy. While generally successful in depleting epithelial progenitors, the depth and severity of injury is difficult to control using chemical-based methods. Moreover, the anterior chamber can be easily perforated while surgically excising the corneal limbus. In the interest of creating a safer and more defined LSCD model, we have therefore evaluated a mechanical debridement technique based upon use of the AlgerBrush II rotating burr. An initial comparison of debridement techniques was conducted in situ using 24 eyes in freshly acquired New Zealand White rabbit cadavers. Techniques for comparison (4 eyes each) included: (1) non-wounded control, (2) surgical limbectomy followed by treatment with 100% (v/v) n-heptanol to remove the corneal epithelium (1-2 minutes), (3) treatment of both limbus and cornea with n-heptanol alone, (4) treatment of both limbus and cornea with 20% (v/v) ethanol (2-3 minutes), (5) a 2.5-mm rounded burr applied to both the limbus and cornea, and (6) a 1-mm pointed burr applied to the limbus, followed by the 2.5-mm rounded burr applied to the cornea. All corneas were excised and processed for histology immediately following debridement. A panel of four assessors subsequently scored the degree of epithelial debridement within the cornea and limbus using masked slides. The 2.5-mm burr most consistently removed the corneal and limbal epithelia. Islands of limbal epithelial cells were occasionally retained following surgical limbectomy/heptanol treatment, or use of the 1-mm burr. Limbal epithelial cells were consistently retained following treatment with either ethanol or n-heptanol alone, with ethanol being the least effective treatment overall. The 2.5-mm burr method was subsequently evaluated in the right eye of 3 live rabbits by weekly clinical assessments (photography and slit lamp examination) for up to 5 weeks, followed by histological analyses (hematoxylin & eosin stain, periodic acid-Schiff stain and immunohistochemistry for keratin 3 and 13). All 3 eyes that had been completely debrided using the 2.5-mm burr displayed symptoms of ocular surface failure as defined by retention of a prominent epithelial defect (~40% of corneal surface at 5 weeks), corneal neovascularization (2 to 3 quadrants), reduced corneal transparency and conjunctivalization of the corneal surface (demonstrated by the presence of goblet cells and/or staining for keratin 13). In conclusion, our findings indicate that the AlgerBrush II rotating burr is an effective method for the establishment of ocular surface failure in New Zealand White rabbits. In particular, we recommend use of the 2.5-mm rotating burr for improved efficiency of epithelial debridement and safety compared to surgical limbectomy.

Inverted slot-mode slow-wave structures for traveling-wave tubes

The dispersion and impedance characteristics of an inverted slot-mode (ISM) slow-wave structure computed by three different techniques, i.e., an analytical model based on a periodic quasi-TEM approach, an equivalent-circuit model, and 3-D electromagnetic simulation are obtained and compared. The comparison was carried out for three different slot-mode structures at S-, C-, and X-bands. The approach was also validated with experimental measurements on a practical X-band ISM traveling-wave tube. The design of ferruleless ISM slow-wave structures, both in circular and rectangular formats, has also been proposed and the predicted dispersion characteristics for these two geometries are compared with 3-D simulation and cold-test measurements. The impedance characteristics for all three designs are also compared.

Investigation of inter-ion interactions in N,N,N',N'-tetramethylethylenediammonium dithiocyanate via experimental and theoretical charge density studies

The crystal structure of the N,N,N',N'-tetramethylethylenediammonium dithiocyanate salt has been examined by experimental charge density studies from high-resolution X-ray diffraction data. The corresponding results are compared with multipole refinements, using theoretical structure factors obtained from a periodic density functional theory calculation at the B3LYP level with a 6-31G** basis set. The salt crystallizes in space group P (1) over bar and contains only a single ion pair with an inversion center in the cation. The salt has thus one unique classical N+-H center dot center dot center dot(NCS)(-) hydrogen bond but also has six other weaker interactions: four C-H center dot center dot center dot S, one C-H center dot center dot center dot N, and one C-H center dot center dot center dot C-pi. The nature of all these interactions has been examined topologically using Bader's quantum theory of "atoms in molecules" and all eight of the Koch-Popelier criteria. The experimental and theoretical approaches agree well and both show that the inter-ion interactions, even in this simplest of systems, play an integrated and complex role in the packing of the ions in the crystal. Electrostatic potential maps are derived from experimental charge densities. This is the first time such a system has been examined in detail by these methods.

Estimation of remaining life of power transformers

Inadvertent failure of power transformers has serious consequences on the power system reliability, economics and the revenue accrual. Insulation is the weakest link in the power transformer prompting periodic inspection of the status of insulation at different points in time. A close Monitoring of the electrical, chemical and such other properties on insulation as are sensitive to the amount of time-dependent degradation becomes mandatory to judge the status of the equipment. Data-driven Diagnostic Testing and Condition Monitoring (DTCM) specific to power transformer is the aspect in focus. Authors develop a Monte Carlo approach for augmenting the rather scanty experimental data normally acquired using Proto-types of power transformers. Also described is a validation procedure for estimating the accuracy of the Model so developed.

Bond-order wave phase, spin solitons, and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J(1) and J(2) between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J(2)/J(1)=0.2411 and is particularly simple at J(2)/J(1)=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap E-m to the lowest-triplet state. The interval 0.4 < J(2)/J(1) < 1.0 has large E-m and small finite-size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large E-m are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility chi(M)(T) is exponentially small for T << E-m and increases nearly linearly with T to a broad maximum. J(1) and J(2) spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

Chemically Programmed Ultrahigh Density Two-Dimensional Semiconductor Superlattice Array

Designing an ultrahigh density linear superlattice array consisting of periodic blocks of different semiconductors in the strong confinement regime via a direct synthetic route remains an unachieved challenge in nanotechnology. We report a general synthesis route for the formulation of a large-area ultrahigh density superlattice array that involves adjoining multiple units of ZnS rods by prolate US particles at the tips. A single one-dimensional wire is 300-500 nm long and consists of periodic quantum wells with a barrier width of 5 nm provided by ZnS and a well width of 1-2 nm provided by CdS, defining a superlattice structure. The synthesis route allows for tailoring of ultranarrow laserlike emissions (fwhm approximate to 125 meV) originating from strong interwell energy dispersion along with control of the width, pitch, and registry of the superlattice assembly. Such an exceptional high-density superlattice array could form the basis of ultrahigh density memories in addition to offering opportunities for technological advancement in conventional heterojunction-based device applications.

Giant magnons in the D1-D5 system

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS(3) x S-3 x T-4. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1 vertical bar 1) x SU(1 vertical bar 1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills Yang-Mills.

Lifting the singular nature of a model for peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. Due to the constraint between the pull force, peel angle and the peel force, the equations of motion derived earlier fall into the category of differential-algebraic equations (DAE) requiring an appropriate algorithm for its numerical solution. By including the kinetic energy arising from the stretched part of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics itself, thus circumventing the need to use any special algorithm. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier singular equations. We find that mass has a strong influence on the dynamics of the model rendering periodic solutions to chaotic and vice versa. Apart from the rich dynamics, the model reproduces several qualitative features of the different waveforms of the peel force function as also the decreasing nature of force drop magnitudes.